(Null hypothesis) H0: Jelly baby colour and habitat type are independent. H1: Jelly baby colour and habitat type are dependent.
Observed Values
Black
Green
Orange
Red
Yellow
Total
Bush 1
1
4
2
7
6
20
Bush 2
1
6
1
5
7
20
Bush 3
2
1
1
1
6
11
Grass 1
5
6
4
3
2
20
Grass 2
7
4
1
3
5
20
Grass 3
5
3
3
4
5
20
Total
21
24
12
23
31
111
In the 'Orange' column, the sampled values are too small, threatening the validity of our results if we were to continue without grouping our categories, based on our combined knowledge about the biology of the jelly baby.
Consequently, we have decided to merge the orange and red data, as the two polymorphic groups are incredibly similar in many aspects.
Black
Green
O + R
Yellow
Total
Bush 1
1
4
9
6
20
Bush 2
1
6
6
7
20
Bush 3
2
1
2
6
11
Grass 1
5
6
7
2
20
Grass 2
7
4
4
5
20
Grass 3
5
3
7
5
20
Total
21
24
35
31
111
We have chosen a standard p value at 0.05, indicating that if the null hypothesis were true, we would expect the probability of getting a result exhibiting differences to this extent or larger to be around 5%. If our chi-squared value exceeds the p value, we may reject the null hypothesis and believe that results are significant.
Chi squared < critical value, therefore the null hypothesis is accepted - Jelly baby colour proportions are independent in grassland habitats.
As both tables show that the colouration is independent, we may assume that selection is not the main driving force in the polymorphism of the jelly baby. It is more likely that a combination of genetic drift and some degree of gene flow is maintaining the distinct polymorphic groups, due to the persistence of variation in all samples, despite no obvious advantage being found.
Furthermore, it is worthwhile to note the very small numbers of jelly babies sampled. With greater numbers, more accuracy may be instilled in statistical tests run from them due to a greater representation of the populations in question. As a general rule of chi-squared statistics, if the expected values are below 5, the sample is too small. To avoid this, groups may be combined to give larger "observed" values, and consequently raising the expected values to something more acceptable within the statistical community. However, the combination of categories, both in colour and habitat, has a chance of over or under emphasising results that were not observed in the original sample. This means that the results from the chi-squared test would be a more fabricated version that, despite giving ease to the calculative process, may misrepresent your findings.
Consequently, our group has only merged colour categories due to necessity, supported by biological knowledge of the jelly baby, and not habitat types.
W.I.P.
Bush Grass Bush Grass Bush Grass
1
Black Green Orange Red Yellow
1 4 2 7 6
2
Black Green Orange Red Yellow
5 6 4 3 2
3
Black Green Orange Red Yellow
1 6 1 5 7
4
Black Green Orange Red Yellow
7 4 1 3 5
5
Green Orange Red Yellow
2 1 11 6
6
Black Green Orange Red Yellow
5 3 3 4 5
Chi-Squared Test
(Null hypothesis) H0: Jelly baby colour and habitat type are independent.
H1: Jelly baby colour and habitat type are dependent.
Observed Values
Consequently, we have decided to merge the orange and red data, as the two polymorphic groups are incredibly similar in many aspects.
We have chosen a standard p value at 0.05, indicating that if the null hypothesis were true, we would expect the probability of getting a result exhibiting differences to this extent or larger to be around 5%. If our chi-squared value exceeds the p value, we may reject the null hypothesis and believe that results are significant.
Habitat Type: Bush
0.86274
2.37255
3.66667
4.09804
11
-0.56863
1.13726
1.68628
-1.37255
-0.66667
-1.66667
-0.45098
1.90196
0.323341.29336
2.84354
1.88389
0.44445
2.77779
0.20338
3.61745
0.206131.49913
0.65919
0.79404
0.06667
0.75758
0.02730
0.88273
Critical value when P is 0.05(1) = 7.82
Chi squared < P therefore the null hypothesis is accepted - Jelly baby colour proportions are independent in bush habitats.
Habitat Type: Grass
G2
G3
7
5
4
3
4
7
5
5
20
20
-1.33333
-0.66667
-0.33333
-1.33333
-2.00000
1.00000
1.00000
1.00000
1.77777
0.44445
0.11111
1.77777
4.00000
1.00000
1.00000
1.00000
0.31372
0.07843
0.02564
0.41025
0.66667
0.16667
0.25000
0.25000
Critical value when P is 0.05(1) = 7.82
Chi squared < critical value, therefore the null hypothesis is accepted - Jelly baby colour proportions are independent in grassland habitats.
As both tables show that the colouration is independent, we may assume that selection is not the main driving force in the polymorphism of the jelly baby. It is more likely that a combination of genetic drift and some degree of gene flow is maintaining the distinct polymorphic groups, due to the persistence of variation in all samples, despite no obvious advantage being found.
Furthermore, it is worthwhile to note the very small numbers of jelly babies sampled. With greater numbers, more accuracy may be instilled in statistical tests run from them due to a greater representation of the populations in question. As a general rule of chi-squared statistics, if the expected values are below 5, the sample is too small. To avoid this, groups may be combined to give larger "observed" values, and consequently raising the expected values to something more acceptable within the statistical community. However, the combination of categories, both in colour and habitat, has a chance of over or under emphasising results that were not observed in the original sample. This means that the results from the chi-squared test would be a more fabricated version that, despite giving ease to the calculative process, may misrepresent your findings.
Consequently, our group has only merged colour categories due to necessity, supported by biological knowledge of the jelly baby, and not habitat types.